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The coproduct in the category of sets is simply the disjoint union with the maps i j being the inclusion maps.Unlike direct products, coproducts in other categories are not all obviously based on the notion for sets, because unions don't behave well with respect to preserving operations (e.g. the union of two groups need not be a group), and so coproducts in different categories can be ...
The plastic used in plastic shopping bags also started as a by-product of oil refining. [1] By-products are sometimes called co-products to indicate that although they are secondary, they are desired products. For example, hides and leather may be called co-products of beef production. There is no strict distinction between by-products and co ...
reconstructed and released by OPenn as Free Cultural Works: CC BY [8] [9] [10] Free Culture: 2004: by Lawrence Lessig (the first CC licensed book released by a major mainstream publisher, Penguin Books) CC BY-NC 1.0 [11] Freesouls: 2008: 2010 (digital ebook) book with essays and photos of key people of the free movement by Joi Ito: CC BY [12 ...
Much of chemistry research is focused on the synthesis and characterization of beneficial products, as well as the detection and removal of undesirable products. Synthetic chemists can be subdivided into research chemists who design new chemicals and pioneer new methods for synthesizing chemicals, as well as process chemists who scale up chemical production and make it safer, more ...
Key principles include atom economy, which aims to incorporate all reactant atoms into the final product, and the reduction of waste and inefficiencies in chemical processes. Innovations in green chemistry, contribute to more sustainable and efficient chemical synthesis, reducing the environmental and health impacts of traditional methods. [7]
In a preadditive category, every finitary product is necessarily a coproduct, and hence a biproduct, and conversely every finitary coproduct is necessarily a product (this is a consequence of the definition, not a part of it). The empty product, is a final object and the empty product in the case of an empty diagram, an initial object. Both ...
Image credits: mleclerc182 #9. Lime green skittles. sour apple is for a*****s. #10. There was a pancake batter in a whipped cream can I used to buy. It was great, you didn’t need to make a ton ...
The Curtin–Hammett principle is a principle in chemical kinetics proposed by David Yarrow Curtin and Louis Plack Hammett.It states that, for a reaction that has a pair of reactive intermediates or reactants that interconvert rapidly (as is usually the case for conformational isomers), each going irreversibly to a different product, the product ratio will depend both on the difference in ...